MadSci Network: Physics
Query:

Re: What is the speed of electricity in numbers?(ex: Light is186,000milespersec

Date: Wed Apr 7 17:31:55 1999
Posted By: Michael Baker, Staff, Environmental Science and Waste Technology, Los Alamos National Laboratory
Area of science: Physics
ID: 921200137.Ph
Message:

In the classical model of electric conduction, a conductor (ie. 
metal bar, wire, etc.) is pictured as a three dimensional array 
of atoms or ions and the electrons are free to move about the 
conductor.  In the absence of an electric field the elctrons 
move about in the same manner as gas molecules move about in a 
container.  The free electrons collide with ions of the 3-D 
array and are in thermal equilibrium with them.    The speed 
with which the electrons are "bouncing" around is on the order
of 10^7 cm/s.

When a potential is electric field is applied, the electron 
experiences a force and subsequently it is accelerated.  The 
velocity of that electron is proportional to the force and the 
duration that the force is applied.  It is inversely proportional
to the mass of the electron.

velocity = q * E * t / m

where q is the charge, E the field strength, t the duration, and
m the mass.  So in other words there is no "constant" speed for
electricity.

The net speed with which electrons travel under some field is 
called the drift velocity. Here is an example of how to calculate 
the drift velocity for electrons in a conductor carrying current:


example
-------
Say you have a piece of 14 gauge copper wire (radius 0.0814 cm)
and that wire is carrying 1 A.  We can assume one free electron 
for every copper atom in the wire.  The density of free electrons 
in the wire, n, is

n = (6.02 x 10^23 atoms/mol)(8.92 g/cc) / 63.5 g/mol

  = 8.46 x 10^22 atoms/cc

and the drift velocity, v, is

v = 1 C/s / (pi * 0.0814 cm * 0.0814 cm)(8.46x10^22 atoms/cc)(1.6x10^-19 C)

  = 3.55 x 10^-3 cm/s

  = 0.00255 cm/s

Note that this drift velocity is very small when compared to the 
velocity the electron at thermal equilibrium is at "bouncing"
around.

[Moderator note:   Another way to look at this is from the perspective of an 
electron.  For the wire mentioned above, when the current flows, it is just one 
electron being pushed into the wire at one end, and another electron popping out 
the other end, over and over many times a second.  The electrons in between 
shift over with a speed of 0.00255 cm/s.  However, the speed of the "push" is 
close to the speed of light, so that the electron on the far end of the wire 
pops out very soon after the electron on the other end is pushed in. I think 
your question brings up the additional question of what exactly electricity is. 
Is it the electrons, or the movement of electrons?]



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